Sight distance is one of the major elements that must be considered in the geometric design to achieve safe and comfortable highways. Daytime sight distance has been extensively studied, and analytical models for two-dimensional (2-D) and three-dimensional (3-D) alignments have been developed. However, nighttime (headlight) sight distance has received less attention. Despite the higher accident rate during nighttime than during daytime, existing analytical models evaluating headlight sight distance are very primitive. Moreover, the interaction between the horizontal and vertical alignments has not been modeled. A four-phase analytical model for headlight sight distance on 3-D combined alignments is presented. The model is an application of the finite-element technique in highway geometric design. The model can determine the maximum distance that can be covered by the vehicle's headlights and that is not obstructed by any sight obstructions including the road surface. On the basis of this analytical model, computer software was developed and used in a preliminary application for 3-D headlight sight distances on a sag or crest vertical curve combined with a horizontal curve. The application showed that the 3-D sight distance on sag vertical curves was generally lower than the corresponding 2-D value when the sag curve was overlapping with a horizontal curve. On the other hand, the overlapping of horizontal curves with crest vertical curves enhanced the 3-D sight distance. The difference between 2-D and 3-D sight distance values in both cases increased with a decrease in the horizontal curve radius and an increase in the pavement cross slope. The model was proved to be extremely valuable in establishing 3-D highway geometric design standards.

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Series Transportation Research Record
Hassan, Y, Easa, S.M. (Said M.), & Halim, A.O. (1997). Modeling headlight sight distance on three-dimensional highway alignments. Transportation Research Record.